# Full text of "Mathematical And Physical Papers - Iii"

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i
182         ON THE COLOURS OF THICK PLATES.
while to take any measures, but contented myself with observing that when the eye was in the expected position, or thereabouts, the rings expanded indefinitely when the image was kept in the centre of the system, and the bands formed when the image was allowed to pass to one side changed curvature as the head moved backwards and forwards.
21. The bands may be considered as completely characterized by the position and magnitude of the achromatic line, and by the value of the numerical quantity which has been already defined as the central order. A simple geometrical construction has already been given for determining the achromatic circle. Substituting X, Y for x, y in (26), and denoting the resulting value of R by — nQ\ we find
....(30).
In the application of this formula n0 is to be taken positively.
Denoting as before the radius of the achromatic circle by vt we find from (28), (29), and the formulae thence derived which give
^ _ \h \c     pi    c \h    pj)      (k Vc     p)    c \h    p
^              _
c) U   c
When the bands are nearly straight, instead of the central order it is more convenient to consider the mean breadth of a fringe. According to the definition of &
since the radii of the several rings are as the square roots of their orders.    We have therefore
22. In the case of a concave mirror, if a small flame be so placed as to coincide with its image, and be then moved a little towards the mirror, or from it, it is possible to see a single